There had been speculation that the Ligue 1 strugglers were set to sack the France World Cup winner and replace him with predecessor Leonardo Jardim.
The 2017 French champions are in the relegation zone after five wins in 20 games under Henry, hired in October.
Franck Passi, appointed as Henry’s assistant on 20 December, will take training on Friday, the club said.
Passi has previously had spells as caretaker manager of Marseille and Lille.
Henry had apologised for using foul language to insult Strasbourg defender Kenny Lala during his side’s 5-1 defeat on Saturday.
Arsenal’s all-time leading scorer is in his first managerial role, having previously been Belgium assistant boss.
He had been on the shortlist for the Aston Villa’s manager’s job in October before taking the job at the club where he started his playing career.